A Multi-Objective Genetic Algorithm Based on Fitting and Interpolation

Considering the diversity of uniform distribution for the solutions of multi-objective optimization problems, we propose the multi-objective genetic algorithm based on fitting (MOGA/F) and interpolation (MOGA/I). The selected operator is based on the optimal reference points uniformly distributed in the objective space, which is calculated by applying a fitting function or interpolation method from a finite set of objective values. After sorting the ranks of the population, the objective space for the last front can be easily calculated by using fitting and interpolation functions, and the uniformly distributed points can be obtained without parameter setting. The individuals with the shortest Euclidean distance to the reference points are chosen according to the error matrix. This method can maintain the diversity and spread of the solutions without destroying the convergence. In this paper, MOGA/F and MOGA/I are compared with the traditional methods, non-dominated sorting genetic algorithm-II and multi-objective evolutionary algorithm based on decomposition, by optimizing the mathematical problems. The numerical examples show that MOGA/F and MOGA/I have a much higher performance in terms of diversity and convergence of the final solutions.